integral ((2x+1))/((x^2+1))

Lösung

integral

\frac{( 2 x + 1 )}{( x ^{2} + 1 )}

ln x^{2} + 1 + arctan (x) + C

Schritte zur Lösung

\int \frac{2 x + 1}{x ^{2} + 1} d x

Multipliziere aus

\frac{2 x + 1}{x ^{2} + 1} : \frac{2 x}{x ^{2} + 1} + \frac{1}{x ^{2} + 1}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{2 x}{x ^{2} + 1} d x + \int \frac{1}{x ^{2} + 1} d x

\int \frac{2 x}{x ^{2} + 1} d x = ln x^{2} + 1

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

= ln x^{2} + 1 + arctan (x)

Füge eine Konstante zur Lösung hinzu

= ln x^{2} + 1 + arctan (x) + C

in t e g r a l sin (2 x - y)

in t e g r a l \frac{1}{2 sin ( 2 x )}

in t e g r a l \frac{x ^{3}}{( x ^{2} + x + 2 )}

in t e g r a l ln (x - 1)

in t e g r a l sin (\frac{x}{3})